Method and apparatus for measuring parameters of a fluid flowing within a pipe using a configurable array of sensors

ABSTRACT

An apparatus for measuring at least one parameter associated with a fluid flowing within a pipe includes a spatial array of pressure sensors disposed at different axial locations x 1 . . . x N  along the pipe. Each of the pressure sensors provides a pressure signal P(t) indicative of unsteady pressure within the pipe at a corresponding axial location of the pipe. A signal processor receives the pressure signals from each of the pressure sensors and determines the parameter of the fluid using pressure signals from selected ones of the pressure sensors. By selecting different pressure sensors, the signal processor can configure the array to meet different criteria. In one embodiment, the array of pressure sensors may be formed on a single sheet of polyvinylidene fluoride (PVDF) that is wrapped around at least a portion of an outer surface of the pipe. This arrangement allows a large number of pressure sensors to be quickly and economically installed.

CROSS-REFERENCE TO RELATED PATENT APPLICATIONS

The present application claims the benefit of U.S. Provisional PatentApplication No. 60/491,824, (CiDRA Docket No. CC-0638) filed Aug. 1,2003, which is incorporated by reference herein in its entirety.

TECHNICAL FIELD

This invention relates to an apparatus for measuring at least oneparameter associated with a fluid flowing within a pipe, and moreparticularly to an apparatus including a configurable array of sensorsfor characterizing unsteady pressures in the fluid for use indetermining at least one parameter associated with the fluid, such asvolumetric flow rate, composition, velocity, mass flow rate, density andparticle size of the fluid and health of a diagnosed component of theflow process.

BACKGROUND

A fluid flow process (flow process) includes any process that involvesthe flow of fluid through pipes, ducts, or other conduits, as well asthrough fluid control devices such as pumps, valves, orifices, heatexchangers, and the like. Flow processes are found in many differentindustries such as the oil and gas industry, refining, food and beverageindustry, chemical and petrochemical industry, pulp and paper industry,power generation, pharmaceutical industry, and water and wastewatertreatment industry. The fluid within the flow process may be a singlephase fluid (e.g., gas, liquid or liquid/liquid mixture) and/or amulti-phase mixture (e.g. paper and pulp slurries or other solid/liquidmixtures). The multi-phase mixture may be a two-phase liquid/gasmixture, a solid/gas mixture or a solid/liquid mixture, gas entrainedliquid or a three-phase mixture.

Various sensing technologies exist for measuring various physicalparameters of single and/or multiphase fluids in an industrial flowprocess. Such physical parameters include, for example, volumetric flowrate, composition, consistency, density, and mass flow rate.

In certain sensing applications, such as in industrial flow processes,it may be desirable sense different parameters at different times and atdifferent locations throughout the industrial flow process. For example,it may be desirable to periodically and temporarily sense volumetricflow at various locations to check the health and performance of theflow process. It may also be desirable to periodically validate theoutput of various meters throughout the flow process. Such requirementstypically require the installation of many different types of flowmeters throughout the flow process. The installation of these differentmeters can be costly and time consuming and may require that a portionof the flow process be shut down to install the sensors.

In any sensing application, it is necessary to detect and replace faultysensors throughout the flow process. Any delay in detecting andreplacing faulty sensors can jeopardize system reliability, and thereplacement of sensors can be a costly and time consuming process.

Thus, there remains a need for a sensor for measuring various parametersof single and/or multiphase fluids in an industrial flow process thatcan be configured to sense different parameters and which reduces thecost and time associated with detecting and replacing faulty components.

SUMMARY OF THE INVENTION

The above-described and other needs are met by a method and apparatusfor measuring a parameter of a fluid passing through a pipe including aspatial array of pressure sensors disposed at different axial locationsalong the pipe. Each of the pressure sensors provides a pressure signalindicative of unsteady pressure within the pipe at a corresponding axiallocation of the pipe. A signal processor receives the pressure signalsfrom each of the pressure sensors, and determines the parameter of thefluid using the pressure signals from selected ones of the pressuresensors. The parameter of the fluid may include, for example, at leastone of: density of the fluid, volumetric flow rate of the fluid, massflow rate of the fluid, composition of the fluid, entrained air in thefluid, consistency of the fluid, size of particles in the fluid, andhealth of a device causing the unsteady pressures to be generated in thepipe.

The signal processor may select the selected ones of the pressuresensors using various criteria. For example: the signal processor mayselect the selected ones of the pressure sensors based on the parameterof the fluid to be output by the signal processor; the selected ones ofthe pressure sensors may be predetermined for the parameter of thefluid; the selected ones of the pressure sensors may be selected inresponse to a previously determined parameter of the fluid; the selectedones of the pressure sensors may be selected in response to an inputsignal; the selected ones of the pressure sensors may be selected inresponse to indication of a faulty pressure sensor; and the selectedones of the pressure sensors may be selected in response to a conditionassociated with the pipe (e.g. vibration).

In another aspect of the invention, an array of, spaced-apart pressuresensors is formed on a single sheet of PVDF. Each of the pressuresensors comprises: a first electrode disposed on a first side of thesheet of PVDF, and a second electrode disposed on a second side of thesheet of PVDF opposite the first electrode. Each of the first and secondelectrodes may be formed as an elongated strip of conductive material.The first and second electrodes may extend around at least a portion ofthe outer surface of the pipe and substantially parallel to adjacentfirst and second electrodes. The elongated strip of conductive materialmay be formed from silver ink applied to the sheet of PVDF, and thefirst and second electrodes may be disposed between layers of anon-conductive material. A connector may be connected to each of thepressure sensors, with the connector being electrically coupled to thesignal processor.

In one embodiment, each of the pressure sensors further comprises: aplurality of electrically connected first electrodes disposed on thefirst side of the sheet of PVDF, and a plurality of electricallyconnected second electrodes disposed on the second side of the sheet ofPVDF opposite the plurality of first electrodes.

The foregoing and other objects, features and advantages of the presentinvention will become more apparent in light of the following detaileddescription of exemplary embodiments thereof.

BRIEF DESCRIPTION OF THE DRAWINGS

Referring now to the drawing wherein like items are numbered alike inthe various Figures:

FIG. 1 is schematic diagram of an apparatus for determining at least oneparameter associated with a fluid flowing in a pipe, the apparatusincluding a configurable array of sensors for characterizing unsteadypressures in the fluid, in accordance with various embodiments of thepresent invention.

FIG. 2 is a block diagram of a method for determining at least oneparameter associated with a fluid flowing in a pipe using a configurablearray of sensors for characterizing the unsteady pressures in the fluid,in accordance with various embodiments of the present invention.

FIG. 3 is a plan view of a portion of the configurable array of sensorsin accordance with various embodiments of the present invention.

FIG. 4 is a cross-sectional elevation view of the configurable array ofsensors taken along section 4-4 of FIG. 3.

FIG. 5 is a plan view of the configurable array of sensors wrappedaround an external surface of the pipe.

FIG. 6 is a plan view of an alternative configurable array of sensors inaccordance with various embodiments of the present invention.

FIG. 7 is a block diagram of a diagnostic logic used in the apparatus ofthe present invention.

FIG. 8 is a block diagram of a first embodiment of a flow logic used inthe apparatus of the present invention.

FIG. 9 is a cross-sectional view of a pipe having coherent structurestherein.

FIG. 10 a kω plot of data processed from an apparatus embodying thepresent invention that illustrates slope of the convective ridge, and aplot of the optimization function of the convective ridge.

FIG. 11 is a block diagram of a second embodiment of a flow logic usedin the apparatus of the present invention.

FIG. 12 a kω plot of data processed from an apparatus embodying thepresent invention that illustrates slope of the acoustic ridges.

FIG. 13 is a plot of mixture sound speed as a function of gas volumefraction for a 5% consistency slurry over a range of process pressures.

FIG. 14 is a plot of sound speed as a function of frequency forair/particle mixtures with fixed particle size and varyingair-to-particle mass ratio.

FIG. 15 is a plot of sound speed as a function of frequency forair/particle mixtures with varying particle size where theair-to-particle mass ratio is fixed.

DETAILED DESCRIPTION

As described in U.S. patent applications Ser. Nos. 10/007,749 (Cidradocket no. CC-00066A), 10/349,716 (Cidra docket no. CC-0579), 10/376,427(Cidra docket no. CC-0596), which are all incorporated herein byreference, unsteady pressures along a pipe, as may be caused by one orboth of acoustic waves propagating through the fluid within the pipeand/or pressure disturbances that convect with the fluid flowing in thepipe (e.g., turbulent eddies and vortical disturbances), contain usefulinformation regarding parameters of the fluid and the flow process.Referring to FIG. 1, an apparatus 10 for measuring at least oneparameter associated with a fluid 13 flowing within a pipe 14 is shown.The parameter of the fluid may include, for example, at least one of:density of the fluid 13, volumetric flow rate of the fluid 13, mass flowrate of the fluid 13, composition of the fluid 13, entrained air in thefluid 13, consistency of the fluid 13, size of particles in the fluid13, and health of a device 34 causing the unsteady pressures to begenerated in the pipe 14. The apparatus 10 includes a spatial array 11of at least two pressure sensors 15 disposed at different axiallocations x₁ . . . x_(N) along the pipe 14. Each of the pressure sensors15 provides a pressure signal P(t) indicative of unsteady pressurewithin the pipe 14 at a corresponding axial location x₁ . . . x_(N) ofthe pipe 14. A signal processor 19 receives the pressure signals P₁(t) .. . P_(N)(t) from the pressure sensors 15 in the array 11, determinesthe parameter of the fluid 13 using pressure signals from selected onesof the pressure sensors 15, and outputs the parameter as a signal 21. Aswill be described in further detail hereinafter, by selecting differentpressure sensors 15, the signal processor 19 can effectively reconfigurethe array 11. As will also be described in further detail hereinafter,the array 11 of pressure sensors 15 may be formed on a single sheet ofpolyvinylidene fluoride (PVDF) that is wrapped around at least a portionof an outer surface of the pipe 14. This arrangement allows a largenumber of pressure sensors 15 to be quickly and economically installed.

While the apparatus is shown as including four pressure sensors 15, itis contemplated that the array 11 of pressure sensors 15 includes two ormore pressure sensors 15, each providing a pressure signal P(t)indicative of unsteady pressure within the pipe 14 at a correspondingaxial location X of the pipe 14. For example, the apparatus may include2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21,22, 23, or 24 pressure sensors 15. Generally, the accuracy of themeasurement improves as the number of sensors in the array increases.The degree of accuracy provided by the greater number of sensors isoffset by the increase in complexity and time for computing the desiredoutput parameter of the flow. Therefore, the number of sensors used isdependent at least on the degree of accuracy desired and the desiredupdate rate of the output parameter provided by the apparatus 10. Thefluid 13 may be a single or multiphase fluid flowing through a duct,conduit or other form of pipe 14.

The signals P₁(t) . . . P_(N)(t) provided by the pressure sensors 15 inthe array 11 are processed by the signal processor 19, which may be partof a larger processing unit 20. For example, the signal processor 19 maybe a microprocessor and the processing unit 20 may be a personalcomputer or other general purpose computer. It is contemplated that thesignal processor 19 may be any one or more signal processing devices forexecuting programmed instructions, such as one or more microprocessorsor application specific integrated circuits (ASICS), and may includememory for storing programmed instructions, set points, parameters, andfor buffering or otherwise storing data.

FIG. 2 is a block diagram of a method 50 employed by processing unit 20for determining the parameter 21 associated with the fluid 13 flowing inpipe 14. Referring to FIGS. 1 and 2, the method 50 begins at block 52with the selection of a group of M pressure sensors 15 from the Npressure sensors 15 in the array 11, where M is a number less than orequal to the number N. The signal processor receives pressure signalsP₁(t) . . . P_(N)(t) from each of the N pressure sensors 15 in the array11 (block 54) and selectively processes the signals from the M selectedpressure sensors 15 to determine the parameter associated with the fluid13 (block 56). The signal processor 19 then provides the parameter as anoutput signal 21 (block 58). While FIG. 2 depicts the step of selectingthe group of M pressure sensors 15 (block 52) as occurring before thereceipt of output signals P₁(t) . . . P_(N)(t) from the array 11 of Npressure sensors 15 (block 54), it is contemplated that the step ofselecting (block 52) may follow the step of receiving (block 54).

To determine the one or more parameters 21 of the flow process, thesignal processor 19 may apply the data from the selected pressuresensors 15 to flow logic 36 executed by signal processor 19. The one ormore parameters 21 may include such parameters as volumetric flow rate,mass flow rate, density, composition, entrained air, consistency,particle size, velocity, mach number, speed of sound propagating throughthe fluid 13, and/or other parameters of the fluid 13. The flow logic 36is described in further detail hereinafter.

The signal processor 19 may also apply one or more of the signals 15and/or one or more parameters 21 from the flow logic 36 to diagnosticlogic 38. Diagnostic logic 38 is executed by signal processor 19 todiagnose the health of any device 34 in the process flow that causesunsteady pressures to be generated in the pipe 14. In FIG. 1, device 34is depicted as a valve; however, it is contemplated that device 34 maybe any machinery, component, or equipment, e.g., motor, fan, pump,generator, engine, gearbox, belt, drive, pulley, hanger, clamp,actuator, valve, meter, or the like. The signal processor 19 may outputone or more parameters 21 indicative of the health of the diagnoseddevice 34. The signal processor may also output a control signal 60 tocontrol the device 34 in response to the parameter 21. The diagnosticlogic 38 is described in further detail hereinafter.

The signal processor 19 may output the one or more parameters 21 to adisplay 24 or another input/output (I/O) device 26. The I/O device 26also accepts user input parameters 48 as may be necessary for the flowlogic 36 and diagnostic logic 38. The I/O device 26, display 24, andsignal processor 19 unit may be mounted in a common housing, which maybe attached to the array 11 by a flexible cable, wireless connection, orthe like. The flexible cable may also be used to provide operating powerfrom the processing unit 20 to the array 11 if necessary.

By selecting different pressure sensors 15, the signal processoreffectively reconfigures the array 11. That is, by adjusting the numberof input signals P (t) used to determine the parameter 21, the signalprocessor 19 effectively adjusts the number of pressure sensors 15 inthe array 11. For example, the signal processor 19 may select three,four, eight, sixteen, twenty four, or N number of sensors pressuresensors 15 and apply the data from the selected pressure sensors todetermine the parameter 21. Generally, the accuracy of the measurementimproves as the number of sensors selected by the signal processor 19increases. The degree of accuracy provided by the greater number ofsensors is offset by the increase in complexity and time for computingthe desired output parameter of the flow. Therefore, the number ofsensors selected is dependent at least on the degree of accuracy desiredand the desire update rate of the output parameter provided by theapparatus 10.

In addition, by selecting pressure sensors 15 that are closer togetheror farther apart along the longitudinal axis of the pipe 14, the signalprocessor 19 effectively adjusts the aperture (distance along the axisof pipe 14) between adjacent sensors 15 in the array 11. For example,the signal processor 19 may select sensors at positions X₁ and X₂ forcloser spacing, and sensors X₁ and X₄ for farther spacing. Also, thesignal processor 19 may select sensors 15 to provide an array of evenlyspaced sensors (e.g., sensors at positions X₁, X₃, X₅, X₇ . . . ) or toprovide an array of unevenly spaced sensors (e.g., sensors at positionsX₁, X₂, X₄, X₇ . . . ).

The microprocessor 19 may reconfigure the array 11 in response to anynumber of criteria. In one embodiment, the signal processor 19 mayselect one or more of the pressure sensors 15 in response to indicationof a faulty pressure sensor 15. For example, the signal processor 19 maycompare the output signal of each pressure sensor 15 to a predeterminedcriteria (e.g., voltage level), and if the output signal indicates thata sensor 15 is faulty (e.g., if the output signal is outside thepredetermined criteria) then the signal processor 19 may disregardoutput signals from the faulty pressure sensor 15. By identifying andeliminating faulty sensors 15, the overall reliability of the apparatus10 is increased. The signal processor 19 may also replace the faultysensor 15 with another sensor 15. For example, if the signal processor19 is applying the signals from an array of eight sensors 15 todetermine the parameter 21 and one of the sensors 15 is determined to befaulty, the signal processor 19 may select a different sensor 15 toreplace the faulty sensor 15 in the array of eight sensors 15.

In another embodiment, the signal processor 19 selects the pressuresensors 15 based on the parameter 21 to be output by the signalprocessor 19. For example, the signal processor 19 may use the outputsignals from one set M of pressure sensors 15 for determining oneparameter 21 (e.g., flow rate) and a different set M of sensors 15 fordetermining another parameter 21 (e.g., speed of sound). This allows thenumber of pressure sensors 15 and the aperture (distance along the axisof pipe 14) between adjacent sensors 15 to be optimized for eachdifferent parameter 21. The set M of sensors 15 for a given parameter 21may be predetermined, or the set M of sensors 15 for a given parameter21 may be determined in response to a previously-determined parameter 21of the fluid 13. For example, if the desired output parameter 15 is theflow rate of the fluid 13, the number and/or aperture of the sensors 15used to determine the flow rate may be adjusted based on a previouslydetermined velocity of the fluid 13. In another example, if a previousattempt at obtaining an output parameter 21 was unsuccessful or providedunacceptable results, the number and/or aperture of the sensors 15 maybe adjusted in attempt to obtain acceptable results. The adjustment inthe number and/or aperture of the sensors 15 can be performed by thesignal processor 19 in real-time.

In another embodiment, the signal processor 19 may select the selectedones of the pressure sensors 15 in response to a signal input via theI/O device 26. The input signal may indicate the parameter 21 to bedetermined by the signal processor 19, in which case the signalprocessor 19 may select the pressure sensors 15 as described above.Alternatively, the input signal may indicate the sensors 15 that are tobe used by the signal processor 19 in determining a particular parameter21. This latter embodiment may be particularly useful by a technician ininstalling or troubleshooting the apparatus 10 or upgrading theapparatus 10 with new functionality.

In yet another embodiment, the signal processor 19 may select theselected ones of the pressure sensors 15 to provide spatial filtering ofconditions associated with the pipe 14. For example, if it is desiredfor the sensors 15 to sense the strain in the pipe 14 due to pressurefluctuations but a large vibration in the pipe 14 exists, the vibrationmay mask the pressure fluctuation signal. By only utilizing sensors 15which are in the nodes of the pipe 14 vibration, then the vibrationbased strains will be minimized and the pressure fluctuation strains canbe measured.

Referring again to FIG. 1, the pressure sensors 15 may includeelectrical strain gages, optical fibers and/or gratings, ported sensors,ultrasonic sensors, among others as described herein, and may beattached to the pipe by adhesive, glue, epoxy, tape or other suitableattachment means to ensure suitable contact between the sensor and thepipe 14. The sensors 15 may alternatively be removable or permanentlyattached via known mechanical techniques such as mechanical fastener,spring loaded, clamped, clam shell arrangement, strapping or otherequivalents. Alternatively, strain gages, including optical fibersand/or gratings, may be embedded in a composite pipe 14. If desired, forcertain applications, gratings may be detached from (or strain oracoustically isolated from) the pipe 14 if desired.

It is also within the scope of the present invention that any otherstrain sensing technique may be used to measure the variations in strainin the pipe 14, such as highly sensitive piezoelectric, electronic orelectric, strain gages attached to or embedded in the pipe 14.

In certain embodiments of the present invention, a piezo-electronicpressure transducer may be used as one or more of the pressure sensorsand it may measure the unsteady (or dynamic or ac) pressure variationsinside the pipe 14 by measuring the pressure levels inside of the pipe.In an embodiment of the present invention, the sensors 14 comprisepressure sensors manufactured by PCB Piezotronics of Depew, N.Y. In onepressure sensor there are integrated circuit piezoelectric voltagemode-type sensors that feature built-in microelectronic amplifiers, andconvert the high-impedance charge into a low-impedance voltage output.Specifically, a Model 106B manufactured by PCB Piezotronics is usedwhich is a high sensitivity, acceleration compensated integrated circuitpiezoelectric quartz pressure sensor suitable for measuring low pressureacoustic phenomena in hydraulic and pneumatic systems. It has the uniquecapability to measure small pressure changes of less than 0.001 psiunder high static conditions. The 106B has a 300 mV/psi sensitivity anda resolution of 91 dB (0.0001 psi).

The pressure sensors 15 may incorporate a built-in MOSFETmicroelectronic amplifier to convert the high-impedance charge outputinto a low-impedance voltage signal. The sensors 15 may be powered froma constant-current source and can operate over long coaxial or ribboncable without signal degradation. The low-impedance voltage signal isnot affected by triboelectric cable noise or insulationresistance-degrading contaminants. Power to operate integrated circuitpiezoelectric sensors generally takes the form of a low-cost, 24 to 27VDC, 2 to 20 mA constant-current supply.

Most piezoelectric pressure sensors are constructed with eithercompression mode quartz crystals preloaded in a rigid housing, orunconstrained tourmaline crystals. These designs give the sensorsmicrosecond response times and resonant frequencies in the hundreds ofkHz, with minimal overshoot or ringing. Small diaphragm diameters ensurespatial resolution of narrow shock waves.

The output characteristic of piezoelectric pressure sensor systems isthat of an AC-coupled system, where repetitive signals decay until thereis an equal area above and below the original base line. As magnitudelevels of the monitored event fluctuate, the output remains stabilizedaround the base line with the positive and negative areas of the curveremaining equal.

Furthermore the present invention contemplates that each of the pressuresensors 15 may include a piezoelectric sensor that provides apiezoelectric material to measure the unsteady pressures of the fluid13. The piezoelectric material, such as the polymer, polarizedfluoropolymer, PVDF, measures the strain induced within the process pipe14 due to unsteady pressure variations within the fluid 13. Strainwithin the pipe 14 is transduced to an output voltage or current by theattached piezoelectric sensors 15.

The PVDF material forming each piezoelectric sensor 15 may be adhered tothe outer surface of a steel strap that extends around and clamps ontothe outer surface of the pipe 14. The piezoelectric sensing element istypically conformal to allow complete or nearly complete circumferentialmeasurement of induced strain. The sensors can be formed from PVDFfilms, co-polymer films, or flexible PZT sensors, similar to thatdescribed in “Piezo Film Sensors technical Manual” provided byMeasurement Specialties, Inc. of Fairfield, N.J., which is incorporatedherein by reference. The advantages of this technique are the following:

-   -   1. Non-intrusive flow rate measurements    -   2. Low cost    -   3. Measurement technique requires no excitation source. Ambient        flow noise is used as a source.    -   4. Flexible piezoelectric sensors can be mounted in a variety of        configurations to enhance signal detection schemes. These        configurations include a) co-located sensors, b) segmented        sensors with opposing polarity configurations, c) wide sensors        to enhance acoustic signal detection and minimize vortical noise        detection, d) tailored sensor geometries to minimize sensitivity        to pipe modes, e) differencing of sensors to eliminate acoustic        noise from vortical signals.    -   5. Higher Temperatures (140 C) (co-polymers)    -   Referring to FIG. 3, in accordance with one aspect of the        present invention, the array 11 of pressure sensors 15 is formed        on a single sheet 62 of PVDF. FIG. 4 shows a cross-sectional        elevation view of a portion of the array 11 of pressure sensors        15, as taken along section 4-4 of FIG. 3. Referring to FIGS. 3        and 4, the sheet 62 of PVDF has a plurality of pressure sensors        15 formed thereon, with each of the pressure sensors 15 being        formed by a first electrode 64 disposed on a first side of the        sheet 62 of PVDF, and a second electrode 66 disposed on a second        side of the sheet 62 of PVDF opposite the first electrode 64. In        the embodiment shown, each of the first and second electrodes        64, 66 is formed as an elongated strip of conductive material of        substantially the same length, width, and thickness. The first        and second electrodes 64, 66 forming each pressure sensor 15 are        substantially parallel to the first and second electrodes 64, 66        forming the adjacent pressure sensors 15.

The first and second electrodes 64, 66 and the sheet 62 of PVDF may bedisposed between layers of a non-conductive material 68, which acts toprotect the PVDF sheet 62 and the electrodes 64, 66 and prevents anelectrical short between the electrodes and any external conductor.

The first and second electrodes 64, 66 may be formed from any flexible,conductive material. Each elongated strip of conductive material formingthe first and second electrodes 64, 66 may be formed from silver inkapplied to the sheet 62 of PVDF. A variety of masking techniques can beused to easily permit the deposition of the electrodes 64 66 only inspecific areas. For example, each elongated strip of conductive materialmay be formed by silk screening a silver ink coating on the sheet 62, Inaddition, the electrode deposition process can be used to route thevarious sensors 15 to a common location for easy attachment to aconnector 70 (FIG. 3) for connection to the signal processor 19 orprocessing unit 20 (FIG. 1).

As shown in FIG. 4, each first and second electrode 64, 66 forms an“active” sensing area 72. The sheet 62 of PVDF also includesnon-sensitive areas 74 separating adjacent active sensing areas 72. Theability to form a plurality of sensors 15 on a single sheet 62 of PVDFis possible due to an interesting property of the PVDF material. Thatis, since the PVDF material is non-conductive, it will create only alocal charge in response to a local strain (or temperature difference).Thus, when conductive electrodes 64, 66 are placed covering an area ofthe PVDF material, it will become an integrating sensor only over thearea covered by the electrodes 64, 66. The non-covered area (i.e., thenon-sensitive areas 74) will not influence the charge accumulation inthe active sensing areas 72. This behavior permits multiple independentsensors 15 to be created on a single sheet 62 of PVDF by only applyingthe electrodes 64, 66 in specific areas.

Referring to FIG. 5, the sheet 62 is shown wrapped around an outersurface of the pipe 14 such that each sensor 15 extends radially aroundat least a portion of the outer surface. Each sensor 15 extendssubstantially fully around the outer surface of the pipe 14, whichallows each sensor 15 to sense the circumferential average of unsteadypressures at the corresponding axial location X and, therefore, reducemeasurement errors associated with vibration or bending modes of thepipe 14.

By forming multiple sensors 15 on a single PVDF sheet 62, installationof the sensors 15 is accomplished by simply wrapping the sheet 15 aroundthe pipe 14. The PVDF sheet 62 can be directly wrapped around the pipe14 with an electrically insulative sheet between the sheet 62 and thepipe 14. Alternatively, the PVDF sheet 62 may be attached to the inneror outer surface of a sheet of material (e.g., a stainless steel sheet)which, in turn, is wrapped around and clamped onto the pipe 14, similarto that described in U.S. Pat. No. 10/795,111 (CiDRA Docket No.CC-0731), filed on Mar. 4, 2004, which is incorporated herein byreference. This reduces the time and effort previously associated withinstalling an array 11 of pressure sensors 15 on a pipe 14.

In addition, with the sheet 62 of the present invention, theinstallation and manufacturing costs are substantially the sameregardless of the number of sensors 15 disposed on the sheet 62. Thus,the sheet 62 is particularly advantageous for the apparatus 10 having aconfigurable (selectable) array 11 of pressure sensors 15. By having alarge number of pressure sensors 15, the configurability of the array 11is greatly increased.

Referring to FIG. 6, an alternative embodiment is shown wherein each ofthe pressure sensors 15 includes a plurality of segments 76, with eachsegment 76 being electrically connected to a single connector 70 on theend of the PVDF sheet 62. Each segment 76 is comprised of a plurality ofelectrically connected first electrodes 64 disposed on the first side ofthe sheet 62 of PVDF, and a plurality of electrically connected secondelectrodes 66 disposed on the second side of the sheet 62 of PVDFopposite the plurality of first electrodes 64 as shown in FIG. 4.

Diagnostic Logic

Referring to FIG. 7 the diagnostic logic 38 measures the sensor inputsignals (or evaluation input signals), which may include one or more ofthe signals P₁(t), P₂(t), P₃(t), . . . P_(N)(t) and the parameters 21,at a step 80. Next, the diagnostic logic 38 compares the evaluationinput signals to a diagnostic evaluation criteria at a step 82,discussed hereinafter. Then, a step 84 checks if there is a match, andif so, a step 86 provides a diagnostic signal indicative of thediagnostic condition that has been detected and may also provideinformation identifying the diagnosed device. The diagnostic signal maybe output as a parameter 21.

Where the evaluation input signal is a parameter 21, as may be outputfrom the flow logic 36, the diagnostic evaluation criteria may be basedon a threshold value of the flow signal 24. For example, the thresholdvalue may be indicative of a maximum or minimum sound speed, machnumber, consistency, composition, entrained air, density, mass flowrate, volumetric flow rate, or the like. If there is not a criteriamatch in step 84, the diagnostic logic 38 exits.

Where the evaluation input signal includes one or more signals P₁(t),P₂(t), P₃(t), . . . P_(N)(t), the diagnostic evaluation criteria may bea threshold (maximum or minimum) pressure. Alternatively, the diagnosticevaluation criteria may be based on an acoustic signature, or aconvective property (i.e., a property that propagates or convects withthe flow). For example, the diagnostic logic 38 may monitor the acousticsignature of any upstream or downstream device (e.g., motor, fan, pump,generator, engine, gear box, belt drive, pulley, hanger, clamp,actuator, valve, meter, or other machinery, equipment or component).Further, the data from the array 11 may be processed in any domain,including the frequency/spatial domain, the temporal/spatial domain, thetemporal/wave-number domain, or the wave-number/frequency (k-ω) domainor other domain, or any combination of one or more of the above. Assuch, any known array processing technique in any of these or otherrelated domains may be used if desired.

For example, for three unsteady pressure signals, the equations in thefrequency/spatial domain equation would be:P(x, ω) = A  𝕖^(−𝕚  k_(r)x) + B  𝕖^(+𝕚  k_(l)x);the temporal/spatial domain would be:P(x, t) = (A  𝕖^(−𝕚  k_(r)x) + B  𝕖^(+𝕚  k_(l)x))𝕖^(𝕚  ω  t);and the k-ω domain (taking the spatial Fourier transform) would be:${P\left( {k,\omega} \right)} = {{\frac{1}{2\quad\pi}{\int_{- \infty}^{+ \infty}{{P\left( {x,\omega} \right)}{\mathbb{e}}^{{\mathbb{i}}\quad{kx}}{\mathbb{d}x}}}} = {{{A(\omega)}{\delta\left( {k - \frac{\omega}{a}} \right)}} + {{B(\omega)}{\delta\left( {k + \frac{\omega}{a}} \right)}}}}$where k is the wave number, a is the speed of sound of the material, xis the location along the pipe, co is frequency (in rad/sec, whereω=2πf), and δ is the Dirac delta function, which shows aspatial/temporal mapping of the acoustic field in the k-δ plane.

Any technique known in the art for using a spatial (or phased) array ofsensors to determine the acoustic or convective fields, beam forming, orother signal processing techniques, may be used to provide an inputevaluation signal to be compared to the diagnostic evaluation criteria.

Flow Logic

Velocity Processing

Referring to FIG. 8, an example of flow logic 36 is shown. As previouslydescribed, the array 11 of at least two sensors 15 located at twolocations x₁,x₂ axially along the pipe 14 sense respective stochasticsignals propagating between the sensors 15 within the pipe 14 at theirrespective locations. Each sensor 15 provides a signal indicating anunsteady pressure at the location of each sensor 15, at each instant ina series of sampling instants. One will appreciate that the array 11 mayinclude more than two sensors 15 distributed at locations x₁ . . .x_(N). The pressure generated by the convective pressure disturbances(e.g., eddies 120, see FIG. 9) may be measured through strained-basedsensors 15 and/or pressure sensors 15. The sensors 15 provide analogpressure time-varying signals P₁(t),P₂(t),P₃(t) . . . P_(N)(t) to thesignal processor 19, which in turn applies selected ones of thesesignals P₁(t),P₂(t),P₃(t), . . . P_(N)(t) to the flow logic 36.

The flow logic 36 processes the selected signals P₁(t),P₂(t),P₃(t), . .. P_(N)(t) to first provide output signals (parameters) 21 indicative ofthe pressure disturbances that convect with the fluid (process flow) 13,and subsequently, provide output signals (parameters) 21 in response topressure disturbances generated by convective waves propagating throughthe fluid 13, such as velocity, Mach number and volumetric flow rate ofthe process flow 13.

The signal processor 19 includes data acquisition unit 126 (e.g., A/Dconverter) that converts the analog signals P₁(t) . . . P_(N)(t) torespective digital signals and provides selected ones of the digitalsignals P₁(t) . . . P_(N)(t) to FFT logic 128. The FFT logic 128calculates the Fourier transform of the digitized time-based inputsignals P₁(t) . . . P_(N)(t) and provides complex frequency domain (orfrequency based) signals P₁(ω),P₂(ω),P₃(ω), . . . P_(N)(ω) indicative ofthe frequency content of the input signals. Instead of FFT's, any othertechnique for obtaining the frequency domain characteristics of thesignals P₁(t)-P_(N)(t), may be used. For example, the cross-spectraldensity and the power spectral density may be used to form a frequencydomain transfer functions (or frequency response or ratios) discussedhereinafter.

One technique of determining the convection velocity of the turbulenteddies 120 within the process flow 13 is by characterizing a convectiveridge of the resulting unsteady pressures using an array of sensors orother beam forming techniques, similar to that described in U.S patentapplication, Ser. No. (Cidra's Docket No. CC-0122A) and U.S. patentapplication, Ser. No. 09/729,994 (Cidra's Docket No. CC-0297), filedDec. 4, 200, now U.S. Pat. No. 6,609,069, which are incorporated hereinby reference. A data accumulator 130 accumulates the frequency signalsP₁(ω)−P_(N)(ω) over a sampling interval, and provides the data to anarray processor 132, which performs a spatial-temporal (two-dimensional)transform of the sensor data, from the xt domain to the k-ω domain, andthen calculates the power in the k-ω plane, as represented by a k-ωplot.

The array processor 132 uses standard so-called beam forming, arrayprocessing, or adaptive array-processing algorithms, i.e. algorithms forprocessing the sensor signals using various delays and weighting tocreate suitable phase relationships between the signals provided by thedifferent sensors, thereby creating phased antenna array functionality.In other words, the beam forming or array processing algorithmstransform the time domain signals from the sensor array into theirspatial and temporal frequency components, i.e. into a set of wavenumbers given by k=2π/λ where λ is the wavelength of a spectralcomponent, and corresponding angular frequencies given by ω=2πν.

The prior art teaches many algorithms of use in spatially and temporallydecomposing a signal from a phased array of sensors, and the presentinvention is not restricted to any particular algorithm. One particularadaptive array processing algorithm is the Capon method/algorithm. Whilethe Capon method is described as one method, the present inventioncontemplates the use of other adaptive array processing algorithms, suchas MUSIC algorithm. The present invention recognizes that suchtechniques can be used to determine flow rate, i.e. that the signalscaused by a stochastic parameter convecting with a flow are timestationary and have a coherence length long enough that it is practicalto locate sensor units apart from each other and yet still be within thecoherence length.

Convective characteristics or parameters have a dispersion relationshipthat can be approximated by the straight-line equation,k=ω/u,where u is the convection velocity (flow velocity). A plot of k-ω pairsobtained from a spectral analysis of sensor samples associated withconvective parameters portrayed so that the energy of the disturbancespectrally corresponding to pairings that might be described as asubstantially straight ridge, a ridge that in turbulent boundary layertheory is called a convective ridge. What is being sensed are notdiscrete events of turbulent eddies, but rather a continuum of possiblyoverlapping events forming a temporally stationary, essentially whiteprocess over the frequency range of interest. In other words, theconvective eddies 120 is distributed over a range of length scales andhence temporal frequencies.

To calculate the power in the k-ω plane, as represented by a k-ω plot(see FIG. 10) of either the signals, the array processor 132 determinesthe wavelength and so the (spatial) wavenumber k, and also the(temporal) frequency and so the angular frequency ω, of various of thespectral components of the stochastic parameter. There are numerousalgorithms available in the public domain to perform thespatial/temporal decomposition of arrays of sensors 15.

The present invention may use temporal and spatial filtering toprecondition the signals to effectively filter out the common modecharacteristics P_(common mode) and other long wavelength (compared tothe sensor spacing) characteristics in the pipe 14 by differencingadjacent sensors 15 and retain a substantial portion of the stochasticparameter associated with the flow field and any other short wavelength(compared to the sensor spacing) low frequency stochastic parameters.

In the case of suitable turbulent eddies 120 (see FIG. 9) being present,the power in the k-ω plane shown in a k-ω plot of FIG. 10 shows aconvective ridge 124. The convective ridge represents the concentrationof a stochastic parameter that convects with the flow and is amathematical manifestation of the relationship between the spatialvariations and temporal variations described above. Such a plot willindicate a tendency for k-ω pairs to appear more or less along a line124 with some slope, the slope indicating the flow velocity.

Once the power in the k-ω plane is determined, a convective ridgeidentifier 134 uses one or another feature extraction method todetermine the location and orientation (slope) of any convective ridge124 present in the k-ω plane. In one embodiment, a so-called slantstacking method is used, a method in which the accumulated frequency ofk-ω pairs in the k-ω plot along different rays emanating from the originare compared, each different ray being associated with a different trialconvection velocity (in that the slope of a ray is assumed to be theflow velocity or correlated to the flow velocity in a known way). Theconvective ridge identifier 134 provides information about the differenttrial convection velocities, information referred to generally asconvective ridge information.

The analyzer 136 examines the convective ridge information including theconvective ridge orientation (slope). Assuming the straight-linedispersion relation given by k=ω/u, the analyzer 136 determines the flowvelocity, Mach number and/or volumetric flow, which are output asparameters 21. The volumetric flow is determined by multiplying thecross-sectional area of the inside of the pipe with the velocity of theprocess flow.

Some or all of the functions within the flow logic 36 may be implementedin software (using a microprocessor or computer) and/or firmware, or maybe implemented using analog and/or digital hardware, having sufficientmemory, interfaces, and capacity to perform the functions describedherein.

Speed of Sound (SOS) Processing

Referring to FIG. 11, another example of flow logic 36 is shown. Whilethe examples of FIG. 8 and FIG. 11 are shown separately, it iscontemplated that the flow logic 36 may perform all of the functionsdescribed with reference to FIG. 8 and FIG. 11. As previously described,the array 11 of at least two sensors 15 located at two at least twolocations x₁,x₂ axially along the pipe 14 sense respective stochasticsignals propagating between the sensors within the pipe at theirrespective locations. Each sensor 15 provides a signal indicating anunsteady pressure at the location of each sensor 15, at each instant ina series of sampling instants. One will appreciate that the sensor array11 may include more than two pressure sensors 15 distributed atlocations x₁ . . . x_(N). The pressure generated by the acousticpressure disturbances (e.g., acoustic waves 122, see FIG. 9) may bemeasured through strained-based sensors and/or pressure sensors. Thesensors 15 provide analog pressure time-varying signalsP₁(t),P₂(t),P₃(t), . . . P_(N)(t) to the flow logic 36. The flow logic36 processes the signals P₁(t),P₂(t),P₃(t), . . . P_(N)(t) from selectedones of the sensors 15 to first provide output signals indicative of thespeed of sound propagating through the fluid (process flow) 13, andsubsequently, provide output signals in response to pressuredisturbances generated by acoustic waves propagating through the processflow 13, such as velocity, Mach number and volumetric flow rate of theprocess flow 13.

The signal processor 19 receives the pressure signals from the array 11of sensors 15. A data acquisition unit 138 digitizes selected ones ofthe pressure signals P₁(t) . . . P_(N)(t) associated with the acousticwaves 122 propagating through the pipe 14. Similarly to the FFT logic128 of FIG. 8, an FFT logic 140 calculates the Fourier transform of theselected digitized time-based input signals P₁(t) . . . P_(N)(t) andprovides complex frequency domain (or frequency based) signalsP₁(ω),P₂(ω),P₃(ω), . . . P_(N)(ω) indicative of the frequency content ofthe input signals.

A data accumulator 142 accumulates the frequency signals P₁(ω) . . .P_(N)(ω) over a sampling interval, and provides the data to an arrayprocessor 144, which performs a spatial-temporal (two-dimensional)transform of the sensor data, from the xt domain to the k-ω domain, andthen calculates the power in the k-ω plane, as represented by a k-ωplot.

To calculate the power in the k-ω plane, as represented by a k-ω plot(see FIG. 12) of either the signals or the differenced signals, thearray processor 144 determines the wavelength and so the (spatial)wavenumber k, and also the (temporal) frequency and so the angularfrequency ω, of various of the spectral components of the stochasticparameter. There are numerous algorithms available in the public domainto perform the spatial/temporal decomposition of arrays of sensor units15.

In the case of suitable acoustic waves 122 being present in both axialdirections, the power in the k-ω plane shown in a k-ω plot of FIG. 12 sodetermined will exhibit a structure that is called an acoustic ridge150, 152 in both the left and right planes of the plot, wherein one ofthe acoustic ridges 150 is indicative of the speed of sound traveling inone axial direction and the other acoustic ridge 152 being indicative ofthe speed of sound traveling in the other axial direction. The acousticridges represent the concentration of a stochastic parameter thatpropagates through the flow and is a mathematical manifestation of therelationship between the spatial variations and temporal variationsdescribed above. Such a plot will indicate a tendency for k-ω pairs toappear more or less along a line 150, 152 with some slope, the slopeindicating the speed of sound.

The power in the k-ω plane so determined is then provided to an acousticridge identifier 146, which uses one or another feature extractionmethod to determine the location and orientation (slope) of any acousticridge present in the left and right k-ω plane. The velocity may bedetermined by using the slope of one of the two acoustic ridges 150, 152or averaging the slopes of the acoustic ridges 150, 152.

Finally, information including the acoustic ridge orientation (slope) isused by an analyzer 148 to determine the flow parameters relating tomeasured speed of sound, such as the consistency or composition of theflow, the density of the flow, the average size of particles in theflow, the air/mass ratio of the flow, gas volume fraction of the flow,the speed of sound propagating through the flow, and/or the percentageof entrained air within the flow.

Similar to the array processor 132 of FIG. 8, the array processor 144uses standard so-called beam forming, array processing, or adaptivearray-processing algorithms, i.e. algorithms for processing the sensorsignals using various delays and weighting to create suitable phaserelationships between the signals provided by the different sensors,thereby creating phased antenna array functionality. In other words, thebeam forming or array processing algorithms transform the time domainsignals from the sensor array into their spatial and temporal frequencycomponents, i.e. into a set of wave numbers given by k=2π/λ where λ isthe wavelength of a spectral component, and corresponding angularfrequencies given by ω=2πν.

One such technique of determining the speed of sound propagating throughthe process flow 13 is using array processing techniques to define anacoustic ridge in the k-ω plane as shown in FIG. 12. The slope of theacoustic ridge is indicative of the speed of sound propagating throughthe process flow 13. The speed of sound (SOS) is determined by applyingsonar arraying processing techniques to determine the speed at which theone dimensional acoustic waves propagate past the axial array ofunsteady pressure measurements distributed along the pipe 14.

The flow logic 36 of the present embodiment measures the speed of sound(SOS) of one-dimensional sound waves propagating through the processflow 13 to determine the gas volume fraction of the process flow 13. Itis known that sound propagates through various mediums at various speedsin such fields as SONAR and RADAR fields. The speed of sound propagatingthrough the pipe 14 and process flow 13 may be determined using a numberof known techniques, such as those set forth in U.S. patent applicationSer. No. 09/344,094, filed Jun. 25, 1999, now U.S. Pat. No. 6,354,147;U.S. patent application Ser. No. 10/795,111, filed Mar. 4, 2004; U.S.patent application Ser. No. 09/997,221, filed Nov. 28, 2001, now U.S.Pat No. 6,587,798; U.S. patent application Ser. No. 10/007,749, filedNov. 7, 2001, and U.S. patent application Ser. No. 10/762,410, filedJan. 21, 2004, each of which are incorporated herein by reference.

While the sonar-based flow meter using an array of sensors 15-18 tomeasure the speed of sound of an acoustic wave propagating through themixture is shown and described, one will appreciate that any means formeasuring the speed of sound of the acoustic wave may used to determinethe entrained gas volume fraction of the mixture/fluid or othercharacteristics of the flow described hereinbefore.

The analyzer 148 of the flow logic 36 provides output parameters 21indicative of characteristics of the process flow 13 that are related tothe measured speed of sound (SOS) propagating through the process flow13. For example, to determine the gas volume fraction (or phasefraction), the analyzer 148 assumes a nearly isothermal condition forthe process flow 13. As such the gas volume fraction or the voidfraction is related to the speed of sound by the following quadraticequation:Ax ² +Bx+C=0wherein x is the speed of sound, A=1+rg/rl*(K_(eff)/P−1)−K_(eff)/P,B=K_(eff)/P−2+rg/rl; C=1−K_(eff)/rl*a_(meas){circumflex over ( )}2);Rg=gas density, rl=liquid density, K_(eff)=effective K (modulus of theliquid and pipewall), P=pressure, and a_(meas)=measured speed of sound.

Effectively,

Gas Voulume Fraction (GVF)=(−B+sqrt(B{circumflex over( )}2-4*A*C))/(2*A)

Alternatively, the sound speed of a mixture can be related to volumetricphase fraction (φ_(i)) of the components and the sound speed (a) anddensities (ρ) of the component through the Wood equation.$\frac{1}{\rho_{mix}\alpha_{{mix}_{\infty}}^{2}} = {{\sum\limits_{i = 1}^{N}{\frac{\phi_{i}}{\rho_{i}a_{i}^{2}}\quad{where}\quad\rho_{mix}}} = {\sum\limits_{i = 1}^{N}{\rho_{i}\phi_{i}}}}$

One dimensional compression waves propagating within a process flow 13contained within a pipe 14 exert an unsteady internal pressure loadingon the pipe. The degree to which the pipe displaces as a result of theunsteady pressure loading influences the speed of propagation of thecompression wave. The relationship among the infinite domain speed ofsound and density of a mixture; the elastic modulus (E), thickness (t),and radius (R) of a vacuum-backed cylindrical conduit; and the effectivepropagation velocity (a_(eff)) for one dimensional compression is givenby the following expression: $\begin{matrix}{a_{eff} = \frac{1}{\sqrt{\frac{1}{a_{{mix}_{\infty}}^{2}} + {\rho_{mix}\frac{2R}{Et}}}}} & \left( {{eq}\quad 1} \right)\end{matrix}$

The mixing rule essentially states that the compressibility of a processflow (1/(ρa²)) is the volumetrically-weighted average of thecompressibilities of the components. For a process flow 13 consisting ofa gas/liquid mixture at pressure and temperatures typical of paper andpulp industry, the compressibility of gas phase is orders of magnitudesgreater than that of the liquid. Thus, the compressibility of the gasphase and the density of the liquid phase primarily determine mixturesound speed, and as such, it is necessary to have a good estimate ofprocess pressure to interpret mixture sound speed in terms of volumetricfraction of entrained gas. The effect of process pressure on therelationship between sound speed and entrained air volume fraction isshown in FIG. 13.

As described hereinbefore, the flow logic 36 of the present embodimentincludes the ability to accurately determine the average particle sizeof a particle/air or droplet/air mixture within the pipe 14 and the airto particle ratio. Provided there is no appreciable slip between the airand the solid coal particle, the propagation of one dimensional soundwave through multiphase mixtures is influenced by the effective mass andthe effective compressibility of the mixture. For an air transportsystem, the degree to which the no-slip assumption applies is a strongfunction of particle size and frequency. In the limit of small particlesand low frequency, the no-slip assumption is valid. As the size of theparticles increases and the frequency of the sound waves increase, thenon-slip assumption becomes increasing less valid. For a given averageparticle size, the increase in slip with frequency causes dispersion,or, in other words, the sound speed of the mixture to change withfrequency. With appropriate calibration the dispersive characteristic ofa process flow 13 will provide a measurement of the average particlesize, as well as, the air to particle ratio (particle/fluid ratio) ofthe process flow 13.

In accordance with the present invention the dispersive nature of thesystem utilizes a first principles model of the interaction between theair and particles. This model is viewed as being representative of aclass of models that seek to account for dispersive effects. Othermodels could be used to account for dispersive effects without alteringthe intent of this disclosure (for example, see the paper titled“Viscous Attenuation of Acoustic Waves in Suspensions” by R. L. Gibson,Jr. and M. N. Toksöz), which is incorporated herein by reference. Themodel allows for slip between the local velocity of the continuous fluidphase and that of the particles.

The following relation can be derived for the dispersive behavior of anidealized fluid particle mixture.${a_{mix}(\omega)} = {a_{f}\sqrt{\frac{1}{1 + \frac{\varphi_{p}\rho_{p}}{\rho_{f}\left( {1 + {\omega^{2}\frac{\rho_{p}^{2}v_{p}^{2}}{K^{2}}}} \right)}}}}$In the above relation, the fluid SOS, density (ρ) and viscosity (φ) arethose of the pure phase fluid, v_(p) is the volume of individualparticles and φ_(p) is the volumetric phase fraction of the particles inthe mixture.

Two parameters of particular interest in steam processes andair-conveyed particles processes are particle size and air-to-fuel massratio or steam quality. To this end, it is of interest to examine thedispersive characteristics of the mixture as a function of these twovariables. FIG. 14 and FIG. 15 show the dispersive behavior in relationsto the speed of sound for coal/air mixtures with parameters typical ofthose used in pulverized coal deliver systems.

In particular FIG. 14 shows the predicted behavior for nominally 50 μmsize coal in air for a range of air-to-fuel ratios. As shown, the effectof air-to-fuel ratio is well defined in the low frequency limit.However, the effect of the air-to-fuel ratio becomes indistinguishableat higher frequencies, approaching the sound speed of the pure air athigh frequencies (above ˜100 Hz).

Similarly, FIG. 15 shows the predicted behavior for a coal/air mixturewith an air-to-fuel ratio of 1.8 with varying particle size. This figureillustrates that particle size has no influence on either the lowfrequency limit (quasi-steady ) sound speed, or on the high frequencylimit of the sound speed. However, particle size does have a pronouncedeffect in the transition region.

FIG. 14 and FIG. 15 illustrate an important aspect of the presentinvention. Namely, that the dispersive properties of dilute mixtures ofparticles suspended in a continuous liquid can be broadly classifiedinto three frequency regimes: low frequency range, high frequency rangeand a transitional frequency range. Although the effect of particle sizeand air-to-fuel ratio are inter-related, the predominant effect ofair-to-fuel ratio is to determine the low frequency limit of the soundspeed to be measured and the predominate effect of particle size is todetermine the frequency range of the transitional regions. As particlesize increases, the frequency at which the dispersive properties appeardecreases. For typical pulverized coal applications, this transitionalregion begins at fairly low frequencies, ˜2 Hz for 50 μm size particles.

Given the difficulties measuring sufficiently low frequencies to applythe quasi-steady model and recognizing that the high frequency soundspeed contains no direct information on either particle size orair-to-fuel ratio, it becomes apparent that the dispersivecharacteristics of the coal/air mixture should be utilized to determineparticle size and air-to-fuel ratio based on speed of soundmeasurements.

Some or all of the functions within the flow logic 36 may be implementedin software (using a microprocessor or computer) and/or firmware, or maybe implemented using analog and/or digital hardware, having sufficientmemory, interfaces, and capacity to perform the functions describedherein.

While FIG. 8 and FIG. 11 depict two different embodiments of the flowlogic 36 to measure various parameters of the flow process, the presentinvention contemplates that the functions of these two embodiments maybe performed by a single flow logic 36.

The apparatus of the present invention provides a configurable array ofsensors for use in determining at least one parameter associated with afluid. By using a sheet of PVDF having a plurality of sensors disposedthereon, a large number of sensors, and thus a highly configurablearray, can be manufactured and installed both quickly and economically.

With the present invention, system reliability is increased becauseredundant sensors can be created; if a fault is seen on one sensor,another can be activated to replace it. In addition, latentfunctionality can be created because, with the present invention, thearray can be reconfigured to meet the needs of new features withoutrequiring a new set of sensors to be installed. The present inventionalso allows the array to be configured differently for measuringdifferent parameters or for optimizing measurement of a given parameter.The present invention permits a non-linear aperture by varying thespacing between consecutive sensors in the array. This can be adjustedin real-time to allow for spatial filtering of the signals to overcomeconditions (e.g., vibrations) that may otherwise prevent or inhibit thesensing of unsteady pressures within the fluid.

It should be understood that any of the features, characteristics,alternatives or modifications described regarding a particularembodiment herein may also be applied, used, or incorporated with anyother embodiment described herein.

Although the invention has been described and illustrated with respectto exemplary embodiments thereof, the foregoing and various otheradditions and omissions may be made therein and thereto withoutdeparting from the spirit and scope of the present invention.

1. An apparatus for measuring a parameter of a fluid passing through apipe, the apparatus comprising: a spatial array of pressure sensorsdisposed at different axial locations along the pipe, each of thepressure sensors providing a pressure signal indicative of unsteadypressure within the pipe at a corresponding axial location of the pipe;and a signal processor configured to: receive the pressure signals fromeach of the pressure sensors, and determine the parameter of the fluidusing the pressure signals from selected ones of the pressure sensors.2. The apparatus of claim 1, wherein the parameter of the fluid includesat least one of: density of the fluid, volumetric flow rate of thefluid, mass flow rate of the fluid, composition of the fluid, entrainedair in the fluid, consistency of the fluid, size of particles in thefluid, and health of a device causing the unsteady pressures to begenerated in the pipe.
 3. The apparatus of claim 2, wherein the signalprocessor selects the selected ones of the pressure sensors based on theparameter of the fluid to be output by the signal processor.
 4. Theapparatus of claim 3, wherein the parameter of the fluid to bedetermined by the signal processor is selected by the signal processorin response to an input signal received by the signal processor.
 5. Theapparatus of claim 3, wherein the selected ones of the pressure sensorsare predetermined for the parameter of the fluid to be determined by thesignal processor.
 6. The apparatus of claim 3, wherein the signalprocessor selects the selected ones of the pressure sensors in responseto a previously determined parameter of the fluid.
 7. The apparatus ofclaim 6, wherein the previously determined parameter of the fluidincludes at least one of: density of the fluid, volumetric flow rate ofthe fluid, mass flow rate of the fluid, composition of the fluid,entrained air in the fluid, consistency of the fluid, size of particlesin the fluid, and health of a device causing the unsteady pressures tobe generated in the pipe.
 8. The apparatus of claim 1, wherein thesignal processor selects the selected ones of the pressure sensors inresponse to an input signal.
 9. The apparatus of claim 1, wherein thesignal processor selects the selected ones of the pressure sensors inresponse to indication of a faulty pressure sensor.
 10. The apparatus ofclaim 1, wherein the signal processor selects the selected ones of thepressure sensors in response to a condition associated with the pipe.11. The apparatus of claim 10, wherein the condition associated with thepipe is a vibration of the pipe, and the signal processor selects theselected ones of the pressure sensors such that each of the selectedones of the pressure sensors are positioned in nodes of the vibration.12. The apparatus of claim 1, wherein the spatial array of pressuresensors are formed on a single sheet of PVDF wrapped around at least aportion of an outer surface of the pipe.
 13. The apparatus of claim 12,wherein each of the pressure sensors includes: a first electrodedisposed on a first side of the sheet of PVDF, and a second electrodedisposed on a second side of the sheet of PVDF opposite the firstelectrode.
 14. The apparatus of claim 13, wherein each of the first andsecond electrodes are formed as an elongated strip of conductivematerial.
 15. The apparatus of claim 14, wherein the first and secondelectrodes extend around at least a portion of the outer surface of thepipe and substantially parallel to adjacent first and second electrodes.16. The apparatus of claim 15, wherein the elongated strip of conductivematerial is formed from silver ink applied to the sheet of PVDF.
 17. Theapparatus of claim 13, wherein the sheet of PVDF and the first andsecond electrodes are disposed between layers of a non-conductivematerial.
 18. The apparatus of claim 13, wherein a connector isconnected to each of the pressure sensors, the connector beingelectrically coupled to the signal processor.
 19. The apparatus of claim13, wherein each of the pressure sensors further comprises: a pluralityof electrically connected first electrodes disposed on the first side ofthe sheet of PVDF, and a plurality of electrically connected secondelectrodes disposed on the second side of the sheet of PVDF opposite theplurality of first electrodes.
 20. The apparatus of claim 1, wherein thenumber of pressure sensors in the pressure sensors is equal to one of:2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21,22, 23, and
 24. 21. The apparatus of claim 1, wherein in the pressuresensors are selected from one or more of: electrical strain gages,optical fibers and/or gratings, ported sensors, and ultrasonic sensors.22. A method of measuring a parameter of a fluid passing through a pipe,the method comprising: providing a spatial array of pressure sensorsdisposed at different axial locations along the pipe, each of thepressure sensors providing a pressure signal indicative of unsteadypressure within the pipe at a corresponding axial location of the pipe;receiving the pressure signals from each of the pressure sensors; anddetermining the parameter of the fluid using the pressure signals outputfrom selected ones of the pressure sensors.
 23. The method of claim 22,wherein the parameter of the fluid includes at least one of: density ofthe fluid, volumetric flow rate of the fluid, mass flow rate of thefluid, composition of the fluid, entrained air in the fluid, consistencyof the fluid, size of particles in the fluid, and health of a devicecausing the unsteady pressures to be generated in the pipe.
 24. Themethod of claim 23, further comprising: selecting the selected ones ofthe pressure sensors based on the parameter of the fluid to be output bythe signal processor.
 25. The method of claim 23, further comprising:selecting the parameter of the fluid to be determined in response to aninput signal.
 26. The method of claim 23, wherein the selected ones ofthe pressure sensors are predetermined for the parameter of the fluid.27. The method of claim 23, further comprising: selecting the selectedones of the pressure sensors in response to a previously determinedparameter of the fluid.
 28. The method of claim 27, wherein thepreviously determined parameter of the fluid includes at least one of:density of the fluid, volumetric flow rate of the fluid, mass flow rateof the fluid, composition of the fluid, entrained air in the fluid,consistency of the fluid, size of particles in the fluid, and health ofa device causing the unsteady pressures to be generated in the pipe. 29.The method of claim 22, wherein the selected ones of the pressuresensors are selected in response to an input signal.
 30. The method ofclaim 22, wherein the selected ones of the pressure sensors are selectedin response to indication of a faulty pressure sensor.
 31. The method ofclaim 22, wherein the selected ones of the pressure sensors are selectedin response to a condition associated with the pipe.
 32. The method ofclaim 31, wherein the condition associated with the pipe is a vibrationof the pipe, and the selected ones of the pressure sensors are selectedsuch that each of the selected ones of the pressure sensors arepositioned in nodes of the vibration.
 33. The method of claim 22,wherein the spatial array of pressure sensors are formed on a singlesheet of PVDF wrapped around at least a portion of an outer surface ofthe pipe.
 34. The method of claim 33, wherein each of the pressuresensors includes: a first electrode disposed on a first side of thesheet of PVDF, and a second electrode disposed on a second side of thesheet of PVDF opposite the first electrode.
 35. The method of claim 34,wherein each of the first and second electrodes are formed as anelongated strip of conductive material.
 36. The method of claim 35,wherein the first and second electrodes extend around at least a portionof the outer surface of the pipe and substantially parallel to adjacentfirst and second electrodes.
 37. The method of claim 36, wherein theelongated strip of conductive material is formed from silver ink appliedto the sheet of PVDF.
 38. The method of claim 34, wherein the sheet ofPVDF and the first and second electrodes are disposed between layers ofa non-conductive material.
 39. The method of claim 33, wherein aconnector is connected to each of the pressure sensors, the connectorbeing electrically coupled to the signal processor.
 40. The method ofclaim 33, wherein each of the pressure sensors further comprises: aplurality of electrically connected first electrodes disposed on thefirst side of the sheet of PVDF, and a plurality of electricallyconnected second electrodes disposed on the second side of the sheet ofPVDF opposite the plurality of first electrodes.
 41. The method of claim22, wherein the number of pressure sensors in the pressure sensors isequal to one of: 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17,18, 19, 20, 21, 22, 23, and
 24. 42. The method of claim 22, wherein inthe pressure sensors are selected from one or more of: electrical straingages, optical fibers and/or gratings, ported sensors, and ultrasonicsensors.
 43. An array of spaced-apart pressure sensors formed on asingle sheet of PVDF, each of the pressure sensors comprising: a firstelectrode disposed on a first side of the sheet of PVDF, and a secondelectrode disposed on a second side of the sheet of PVDF opposite thefirst electrode.
 44. The apparatus of claim 43, wherein each of thefirst and second electrodes are formed as an elongated strip ofconductive material.
 45. The apparatus of claim 44, wherein the firstand second electrodes extend substantially parallel to adjacent firstand second electrodes.
 46. The apparatus of claim 45, wherein theelongated strip of conductive material is formed from silver ink appliedto the sheet of PVDF.
 47. The apparatus of claim 43, wherein the sheetof PVDF and the first and second electrodes are disposed between layersof a non-conductive material.
 48. The apparatus of claim 43, wherein aconnector is connected to each of the pressure sensors, the connectorbeing electrically coupled to the signal processor.
 49. The apparatus ofclaim 43, wherein each of the pressure sensors further comprises: aplurality of electrically connected first electrodes disposed on thefirst side of the sheet of PVDF, and a plurality of electricallyconnected second electrodes disposed on the second side of the sheet ofPVDF opposite the plurality of first electrodes.
 50. An apparatus formeasuring a parameter of a fluid passing through a pipe, the apparatuscomprising: an array of pressure sensors formed on a single sheet ofPVDF wrapped around at least a portion of an outer surface of the pipe,each of the pressure sensors including: a first electrode disposed on afirst side of the sheet of PVDF, and a second electrode disposed on asecond side of the sheet of PVDF opposite the first electrode, each ofthe pressure sensors providing a pressure signal indicative of unsteadypressure within the pipe at a corresponding axial location of the pipe;and a signal processor configured to: receive the pressure signals fromeach of the pressure sensors, and determine the parameter of the fluidusing the pressure signals from the pressure sensors.
 51. The apparatusof claim 50, wherein the parameter of the fluid includes at least oneof: density of the fluid, volumetric flow rate of the fluid, mass flowrate of the fluid, composition of the fluid, entrained air in the fluid,consistency of the fluid, size of particles in the fluid, and health ofa device causing the unsteady pressures to be generated in the pipe. 52.The apparatus of claim 50, wherein each of the first and secondelectrodes are formed as an elongated strip of conductive material. 53.The apparatus of claim 52, wherein the first and second electrodesextend circumferentially around at least a portion the outer surface ofthe pipe and substantially parallel to adjacent first and secondelectrodes.
 54. The apparatus of claim 53, wherein the elongated stripof conductive material is formed from silver ink applied to the sheet ofPVDF.
 55. The apparatus of claim 50, wherein the sheet of PVDF and thefirst and second electrodes are disposed between layers of anon-conductive material.
 56. The apparatus of claim 50, wherein aconnector is connected to each of the pressure sensors, the connectorbeing electrically coupled to the signal processor.
 57. The apparatus ofclaim 50, wherein each of the pressure sensors further includes: aplurality of electrically connected first electrodes disposed on thefirst side of the sheet of PVDF, and a plurality of electricallyconnected second electrodes disposed on the second side of the sheet ofPVDF opposite the plurality of first electrodes.